2.19 Both portions of the rod ABC are made of an aluminum for which E = 70 GPa. Knowing that the magnitude of P is 4 kN, determine (a) the value of Q so that the deflection at A is zero, (b) the cor- responding deflection of B. A 20-mm diameter 0.4 m B 0.5 m 60-mm diameter C Fig. P2.19 and P2.20

A plane element removed from a thin-walled cylindrical shell loaded in torsion is subject to the shearing stresses shown in Fig. 3-20. Determine the principal stresses existing in this element and the directions of the planes on which they occur. Ans. 50 MPa at 45° 50 MPa 50 MPa 50 MPa 50 MPa

Both portions of rod ABC are made of aluminum for which E = 70 MPa. Knowing that the magnitude of P = 6 kN and Q = 42 kN determine the diameter d of portion AB for which the deflection of point A will be zero. A - - 0.4 m 0.5 m 60-mm diameter

(b) A cooling tube having the cross section shown in Fig. Q1(b) is formed from a sheet of stainless steel of 3 mm thickness. The radii c₁ = 150 mm and c₂ = 100 mm are measured to the center line of the sheet metal. Knowing that a torque of magnitude T = 3 kNm is applied to the tube, determine (i) the maximum shearing stress in the tube (ii) the magnitude of the torque carried by the outer circular shell Neglect the dimension of the small opening where the outer and inner shells are connected. Hint: q - T 2A q=rt, T = Fr. Fig. Q1(b)